For this achievement you must start from the beginning of the game in co-op and do every Saints, Ronin, Brotherhood, Samedi and Ultor missions. Each mission MUST be done in co-op but it doesn't have to be the same partner each time and it doesn't matter what order you do them in so long as you do them all.
You can check your progress in the statistics section of the pause menu. And you can also check your noticeboard in certain cribs to check which ones you have and haven't done and maybe go back and replay ones you haven't done.
This achievement is reported to be glitchy however when it comes to redoing missions in co-op that you have only done in single player, follow the link below for more details:http://community.saintsrow.com/blogs/?p=305
(this is something which I myself am having problems with but my mate got the achievement so I know the requirements)